Transversal filter with wide band phase shifters in series with the delay cells
The present invention relates to a transversal filter. The invention concerns optimizing the structure of a transversal filter operating at intermediate frequency and used in a time equalizer for digital microwave beams. 
     BACKGROUND OF THE INVENTION 
     High capacity digital microwave beam transmission requiring a large bandwidth per channel is particularly subject to selective fading due to multi-path propagation. The passband required for transmitting each channel can, however, be reduced by using high spectrum efficiency multi-state modulation, thereby optimizing utilization of predetermined frequency allocations. Unfortunately, the complexity of such forms of modulation makes them sensitive to distortion. Transmission degradation gives rise to the appearance of errors, thereby degrading the quality, and in severe cases the availability, of a link. 
     Various remedies may be proposed: 
     frequency diversity: i.e. switching from a disturbed channel to a redundant channel used as a spare. Unfortunately, frequency diversity is insufficient when several channels are disturbed simultaneously; 
     space diversity, which may be constituted by diversity at maximum power, by diversity at minimum distortion, or by diversity by baseband switching. Space diversity is effective (although limited to correcting trouble due to propagation), but it is costly in antennas and consequently in locations on microwave towers; 
     self-adaptive equalization in baseband, i.e. full processing of the signal (in amplitude and in phase), capable of providing correction beyond that required for selective fading due to multiple paths. Such equalization is described in an article entitled &#34;Self-adaptive baseband equalizers for digital microwave beams&#34; by O. de Luca in the Thomson-CSF Technical Journal, volume 16, No. 1, March 1984; 
     self-adaptive equalization at intermediate frequency. Unlike equalization in baseband, both of the paths in quadrature are processed simultaneously, thereby making it possible to obtain structures which are less complicated and thus cheaper in analog embodiments. An equalizer of this type based on the principle of the transversal filter, makes it possible to correct the distortions to which the signal is subject, and in particular those due to multiple paths. 
     The object of the invention is to optimize the structure of a transversal filter operating at intermediate frequency and used in a time equalizer. 
     SUMMARY OF THE INVENTION 
     To this end, the present invention provides a transversal filter comprising: a series connection of M+L delay cells defining M+L+1 signal samples; M+L+1 branches each having a midpoint connected to receive a respective one of said signal samples and first and second multipliers for multiplying its signal sample by respective first and second coefficients; and first and second summing circuits respectively connected to sum the outputs from said first multipliers and from said second multipliers, wherein a wideband phase shifter is associated in series with each delay cell, said phase shifter providing a phase shift δφ such that δφ=Ω O  T (modulo 2π) where Ω O  is the angular frequency of the intermediate carrier and T represents the duration of the delay due to a delay cell which advantageously has the value T=Ts, where Ts represents the duration of one symbol. 
     In a second embodiment, the invention proposes a filter in which each delay cell is connected to the midpoint of a branch of index i by a phase shifter providing a phase shift of value iδφ, where -M≦i≦+L. 
     Advantageously, a filter is made such that M=L=2, with Ω O  Ts=-π/2 (modulo 2π), and the branch of index -2 has a first coefficient -Cp -2  and a second coefficient -Cq -2  ; the branch of index -1 has a first coefficient -Cq -1  and a second coefficient -Cq -1  ; the branch of index +1 has a first coefficient Cp +1  and a second coefficient -Cp +1  ; and the branch of index +2 has a first coefficient -Cp +2  and a second coefficient -Cq +2 . 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Embodiments of the invention are described by way of example with reference to the accompanying drawings, in which: 
     FIG. 1 shows the structure of a prior art transversal filter; 
     FIG. 2 shows a first embodiment of a transversal filter of the invention; 
     FIG. 3 shows a second embodiment of a transversal filter of the invention; 
     FIG. 4 shows a special case of the transversal filter shown in FIG. 3; and 
     FIG. 5 shows another embodiment of a transversal filter of the invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     A transversal filter modifies the signal by a weighted combination of said signal taken at different instants, at successive time intervals T. 
     Such a filter, as shown in FIG. 1, has a central coefficient C O , M complex leading coefficients (with indices -M to -1) for correcting the front part of the impulse response, and L trailing coefficients (having indices from +1 to +L) for correcting the rear portion of the impulse response. 
     This prior art transversal filter comprises M+L+1 branches each having a respective index i, where -M ≦i ≦+L, i.e.: 
     a central branch of index 0; 
     L branches with positive indices +1 to +L; and 
     M branches with negative indices -1 to -M; 
     with each branch comprising, on either side of a midpoint, a first multiplier 10 for multiplying by a respective coefficient Cp i  corresponding to the in-phase signal portion, and a second multiplier 11 for multiplying by a coefficient Cq i  corresponding to the quadrature signal portion. 
     The filter also includes M+L delay cells 12 connected in series with the first cell receiving the input signal E, and with each delay cell 12 being disposed between the midpoints of two adjacent branches. 
     The second ends of the first multipliers 10 are connected to respective inputs of a first summing circuit 13, and the second ends of the second multipliers 11 are connected to respective inputs of a second summing circuit 14, with the output from the first summing circuit being directly connected to a first input of a third summing circuit 15, and with the output from the second summing circuit being connected to a second input of said third summing circuit 15 via a π/2 phase shifter 16, such that the output from the third summing circuit constitutes the output S from said filter, at which output a signal is obtained constituting a weighted sum of the input signal E subjected to successive delays in M+L cells each imparting a delay T. 
     Consider the following notation: 
     C k  =Cp k  +jCq k  i.e. the complex coefficient of index k in the transversal filter. The transversal filter has a central coefficient C O  such that C O  =Cp O  +jCq O , M leading coefficients (from -M to -1), and L trailing coefficients (from +1 to +L). 
     Ze(t)=Xe(t)+jYe(t) is the emitted baseband signal (prior to filtering) at time. 
     Sr(t)=(Xr(t)+jYr(t)).EXP(jΩ O  t)=Zr(t).EXP(jΩ O  t) is the signal present on reception at time corresponding to the coefficient C O  of the transversal filter, with filtering being performed at intermediate frequency, as shown in FIG. 1, with Ω O  being the angular frequency of the intermediate frequency carrier. (In order to simplify writing down the equations, no account is taken herein of the time delay between transmission and reception, but that does not reduce the generality of the description.) 
     The signal at the output from the transversal filter can be written: ##EQU1## where T is a fixed delay which is usually taken to be equal to the symbol time Ts, then ##EQU2## Let the quantity ##EQU3## be written Zc(t) which constitutes the complex representation in baseband of the equalized received signal. 
     The coefficients C k  for obtaining the best possible reception of the transmitted signal are calculated using an algorithm derived from the gradient algorithm for k varying from -M to +L: 
     
         C.sub.k.sup.i+1 =C.sub.k.sup.i -μ.E.sub.i.Ze.sub.i-k.sup.*.EXP(jkΩ.sub.O T) 
    
     for k varying from -M to +L, where: 
     C k   i  is the complex coefficient of index k taken at instant t=iTs; 
     μ is the algorithm step size (constant); 
     E i  =Ep i  +j.Eq i  is the complex error signal at the instant t=i.Ts (giving Ei=Zc(t=i.T) - Ze(t=i.T)); and 
     Ze i-k   *  is the complex conjugate of the emitted signal at instant t=(i - k).Ts thus giving the regenerated signal as: 
     
         D.sub.i =Xc(t=i.Ts)+jyc(t=i.Ts) 
    
     where the symbol   represents the decision taken during regeneration. When equalization is correctly performed, the signal regenerated on reception at the characteristic instants is equal to the transmitted signal: 
     
         D.sub.i =Ze(t=i.Ts) 
    
     It is common practice to modify the algorithm giving C k   i+1  as follows 
     
         C.sub.k.sup.i+1 =C.sub.k.sup.i -μ.E.sub.i.D.sub.i-k.sup.*.EXP(jkΩ.sub.O T) 
    
     where 
     E i  =Zc(t=i.Ts) - D i   
     and then as follows: 
     
         C.sub.k.sup.i+1 =C.sub.k.sup.i -μ.sgn(E.sub.i).sgn(D.sub.i-k.sup.*.EXP(jkΩ.sub.O T)) 
    
     where sgn(a+j.b)=sgn(a)+j.sgn(b) for real a and b (where sgn(a)=the sign of a). 
     It appears that the terms in EXP(jkΩ O  T) complicate practical implementation of the algorithm. 
     The equalizers currently used with microwave beams are synchronous equalizers for which T=Ts, where Ts represents the duration of one symbol. 
     A first way of simplifying EXP(jkΩ O  T) consists in ensuring that Ω O  T=Ω O  Ts=N.2π where N is an arbitrary integer. An example of an implementation is described in the article entitled &#34;6 GHz 135 MBPS digital radio system with 64 QAM modulation&#34; by T. Noguchi, T. Ryu, Y. Koizumi, S. Mizoguchi, M. Yoshimoto, K. Nakamura published in ICC 1983, pp. 1472 to 1477, in which the framed data rate 6/Ts is adjusted to satisfy the equation Ω O  Ts=6π. That gives EXP(jkΩ O  T)=1 for all values of k, thereby simplifying the algorithm for C k   i+1 , giving: 
     
         C.sub.k.sup.i+1 =C.sub.k.sup.i- μ.sgn(E.sub.i).sgn(D.sub.i-k.sup.*) 
    
     A second way of simplifying EXP(jkΩ O  T) when Ω O  Ts=(N+ε).2π, where ε is about 1/100 or -1/100, consists in performing Ω O  T=N.2π, i.e. in using a practical delay T which is very slightly different from Ts, in which case performance degradation is not very significant. 
     However, these solutions suffer from various drawbacks: in the first solution, Ω O  Ts can be adjusted only by using a framed data rate greater than the line data rate. Indeed, this increase in data rate is common practice in digital microwave beams for several reasons: to make it possible to use or add auxiliary channels, when using error correcting codes which increase data rate, etc. However, it is desirable that this increase in data rate should not have to satisfy the condition Ω O  Ts=N.2π which is very stringent, since in practical cases that gives only one possibility at best for Ts. 
     The second solution can be envisaged only in fairly specific cases: for example framed data rates close to 140 Mbit/s for 16 state quadrature amplitude modulation (QAM) or for 64 QAM or for 256 QAM, with intermediate frequencies of 70 MHz or 140 MHz, giving N=2, 3, 4, 6, or 8. In addition, performance is slightly degraded compared with the optimum. 
     The object of the present invention is to make it possible to have Ω O  and Ts which are independent from each other while making use of the simplicity of the last algorithm for obtaining C k   i+1 . 
     The invention consists in using wideband phase shifters 17 which compensate the terms in EXP(-jkΩ O  T) in the expression for Sc(t); with each phase shifter 17 being connected in series with a delay cell 12, as shown in FIG. 2. 
     δφ is a wideband phase shifter such that EXP(jδφ)=EXP(jΩ O  Ts), i.e. such that δφ=Ω O  Ts(modulo 2π). 
     The baseband signal is then written: ##EQU4## and the coefficient-controlling algorithm is written: 
     
         C.sub.k.sup.i+1 = 
    
     
         C.sub.k.sup.i -μ.sgn(E.sub.i).sgn(D.sub.i-k.sup.*) 
    
     which is then easily implemented. 
     A second embodiment is shown in FIG. 3. The delay cells 12 are still connected in series, but they are connected to the midpoints of the various branches of index i via phase shifters 18 providing a shift of value iδφ, with each phase shifter of value iδφ being connected to the branch of index i, where -M≦i≦+L. 
     Although this implementation appears more complex, a priori, it has a major practical advantage when Ω O .Ts=O(modπ/2), since it is then possible to use a π/2 phase shifter which is already included in the circuit. A practical example of such an embodiment is shown in FIG. 4 for an equalizer where M=L=2, and Ω O .Ts=-π/2 (mod 2π). 
     It can be seen that the in-phase coefficients (Cp) and the quadrature coefficients (Cq) can then either remain in their original branches (possibly with a change of sign), or else they may be moved to the branch which is in quadrature therewith (possibly with a change of sign). The phase shifters for shifting π/2, -π/2, π, etc. ... can thus be made in a manner which is particularly simple and attractive. 
     The filter is then such that the branch of index -2 has a first coefficient -Cp -2  and a second coefficient -Cq -2  ; the branch of index -1 has a first coefficient -Cq -1  and a second coefficient Cp -1  ; the branch of index +1 has a first coefficient Cq +1  and a second coefficient -Cp +1  ; and the branch of index +2 has a first coefficient -Cp +2  and a second coefficient -Cq +2 . 
     It is important to note that this solution is also highly advantageous in practice when the value of Ω O .Ts is close to O(mod π/2). 
     Transversal filters include recursive filters which have one or more feedback loops and which therefore have an infinite impulse response, and non-recursive filters which have a finite impulse response, since they have no loops. 
     A transversal filter having a direct portion and a recursive portion is described at page 138 of the abovementioned article by O. de Luca entitled &#34;Self-adaptive baseband equalizers for digital microwave beams&#34;. 
     Such a transversal filter may be implemented using the filter of the invention. Thus, FIG. 5 shows a filter with a leading transversal portion 20 and a trailing recursive portion 21. This filter uses the same elements as shown in FIG. 2, with the elements of the leading transversal portion having an index a, and those of the trailing recursive portion having an index b. 
     Thus, the recursive portion 21 has a direct portion whose signal is successively delayed in N cells 12b providing a delay T, each of which is associated with a phase shifter 17b. The weighted sum of these delayed signals is then looped back via an input summing circuit 15b. 
     Naturally, the invention has been described and shown purely by way of preferred example, and its component elements could be replaced by equivalent elements without thereby going beyond the scope of the invention. 
     Thus, the transverse filter of FIG. 5 having a direct portion and a recursive portion, could equally well be based on the filters shown in FIGS. 3 and 4.